Anomalous Structures of Fisher Zero Lines in Biorthogonal Dynamical Quantum Phase Transitions

Abstract

Fisher zero lines of the Loschmidt amplitude in non-Hermitian quenches can exhibit anomalous structures in the complex time plane, such as divergence, separation, and the restriction of all branches or a specific branch to the real or imaginary axis. Here, we use the biorthogonal framework to reveal the origin of these structures and determine the corresponding critical momentum conditions by analyzing the values of m_k=ĥ₀·ĥ₁, the dot product between the normalized prequench and postquench complex Bloch vectors. When Fisher zeros continuously cover the real-time axis, the density of Fisher zeros is further introduced to identify the critical times within these critical regions, at which the rate function becomes nonanalytic. We verify our results in a generalized non-Hermitian SSH model by quenching the Peierls phase and the non-Hermitian gain-loss strength, and also use the Jordan form to analyze the dynamics at postquench exceptional points, where the conventional Fisher zero formula is not applicable.

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BibTeX RIS

BibTeX

@misc{nie2026anomalous,
  title = {{Anomalous Structures of Fisher Zero Lines in Biorthogonal Dynamical Quantum Phase Transitions}},
  author = {Wen-Hui Nie and Chong Li and Lin-Cheng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36521},
  eprint = {2610.36521},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36521},
}

RIS

TY  - UNPB
TI  - Anomalous Structures of Fisher Zero Lines in Biorthogonal Dynamical Quantum Phase Transitions
AU  - Wen-Hui Nie
AU  - Chong Li
AU  - Lin-Cheng Wang
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36521
UR  - https://arxiv.org/abs/2610.36521
AB  - Fisher zero lines of the Loschmidt amplitude in non-Hermitian quenches can exhibit anomalous structures in the complex time plane, such as divergence, separation, and the restriction of all branches or a specific branch to the real or imaginary axis. Here, we use the biorthogonal framework to reveal the origin of these structures and determine the corresponding critical momentum conditions by analyzing the values of m_k=ĥ_0·ĥ_1, the dot product between the normalized prequench and postquench complex Bloch vectors. When Fisher zeros continuously cover the real-time axis, the density of Fisher zeros is further introduced to identify the critical times within these critical regions, at which the rate function becomes nonanalytic. We verify our results in a generalized non-Hermitian SSH model by quenching the Peierls phase and the non-Hermitian gain-loss strength, and also use the Jordan form to analyze the dynamics at postquench exceptional points, where the conventional Fisher zero formula is not applicable.
ER  -

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